Extensions 1→N→G→Q→1 with N=C₂³×D₅ and Q=S₃

Direct product G=N×Q with N=C₂³×D₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₂³×D₅		120		S3xC2^3xD5	480,1207

Semidirect products G=N:Q with N=C₂³×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂³×D₅)⋊₁S₃ = D₁₀⋊S₄	φ: S₃/C₁ → S₃ ⊆ Out C₂³×D₅	60	6	(C2^3xD5):1S3	480,980
(C₂³×D₅)⋊₂S₃ = A₄⋊D₂₀	φ: S₃/C₁ → S₃ ⊆ Out C₂³×D₅	60	6+	(C2^3xD5):2S3	480,981
(C₂³×D₅)⋊₃S₃ = C₂×D₅×S₄	φ: S₃/C₁ → S₃ ⊆ Out C₂³×D₅	30	6+	(C2^3xD5):3S3	480,1193
(C₂³×D₅)⋊₄S₃ = (C₂×C₃₀)⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5):4S3	480,639
(C₂³×D₅)⋊₅S₃ = (C₂×C₆)⋊₈D₂₀	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5):5S3	480,640
(C₂³×D₅)⋊₆S₃ = C₂²×C₁₅⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	240		(C2^3xD5):6S3	480,1118
(C₂³×D₅)⋊₇S₃ = C₂²×C₃⋊D₂₀	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	240		(C2^3xD5):7S3	480,1119
(C₂³×D₅)⋊₈S₃ = C₂×D₅×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5):8S3	480,1122

Non-split extensions G=N.Q with N=C₂³×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂³×D₅).₁S₃ = D₅×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Out C₂³×D₅	60	6	(C2^3xD5).1S3	480,979
(C₂³×D₅).₂S₃ = C₂×A₄⋊F₅	φ: S₃/C₁ → S₃ ⊆ Out C₂³×D₅	30	12+	(C2^3xD5).2S3	480,1191
(C₂³×D₅).₃S₃ = C₂×D₁₀⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	240		(C2^3xD5).3S3	480,611
(C₂³×D₅).₄S₃ = D₅×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5).4S3	480,623
(C₂³×D₅).₅S₃ = C₂×D₁₀.D₆	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5).5S3	480,1072
(C₂³×D₅).₆S₃ = C₂³×C₃⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₂³×D₅	120		(C2^3xD5).6S3	480,1206
(C₂³×D₅).₇S₃ = C₂²×D₅×Dic₃	φ: trivial image	240		(C2^3xD5).7S3	480,1112

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